Yazar "Bayram, Nilay Sahin" seçeneğine göre listele

Listeleniyor 1 - 6 / 6
  • [ X ]
    Öğe
    An extension of Korovkin theorem via power series method
    (Springer Basel Ag, 2022) Yildiz, Sevda; Bayram, Nilay Sahin
    In the present work, using the power series method, we obtain various Korovkin-type approximation theorems for linear operators defined on derivatives of functions. We also explain that our theorem makes more sense with a striking example. We study the quantitative estimates of linear operators. In the final section, we summarize our new results.
  • [ X ]
    Öğe
    Approximation by statistical convergence with respect to power series methods
    (Hacettepe Univ, Fac Sci, 2022) Bayram, Nilay Sahin; Yildiz, Sevda
    In the present work, using statistical convergence with respect to power series methods, we obtain various Korovkin-type approximation theorems for linear operators defined on derivatives of functions. Then we give an example satisfying our approximation theorem. We study certain rate of convergence related to this method. In the final section we summarize these results to emphasize the importance of the study.
  • [ X ]
    Öğe
    Approximation theorems via Pp-statistical convergence on weighted spaces
    (Walter De Gruyter Gmbh, 2024) Yildiz, Sevda; Bayram, Nilay Sahin
    In this paper, we obtain some Korovkin type approximation theorems for double sequences of positive linear operators on two-dimensional weighted spaces via statistical type convergence method with respect to power series method. Additionally, we calculate the rate of convergence. As an application, we provide an approximation using the generalization of Gadjiev-Ibragimov operators for P-p-statistical convergence. Our results are meaningful and stronger than those previously given for two-dimensional weighted spaces.
  • [ X ]
    Öğe
    Construction of Bivariate Modified Bernstein-Chlodowsky Operators and Approximation Theorems
    (Padova Univ Press, 2023) Yildiz, Sevda; Bayram, Nilay Sahin
    In this paper, we modified Bernstein-Chlodowsky operators via weaker condition than the classical Bernstein-Chlodowsky operators' condition. We get more powerful results than classical ones. We obtain aproximation properties for these positive linear operators and their generalizations in this work. The rate of convergence of these operators is calculated by means of the modulus of continuity and Lipschitz class of the functions off of two variables. Finally, we give some concluding remarks with q-calculus.
  • [ X ]
    Öğe
    On P-equi-statistical relative convergence in sequences of fuzzy-valued functions with applications to Korovkin-type approximation
    (Univ Nis, Fac Sci Math, 2025) Yildiz, Sevda; Bayram, Nilay Sahin
    In this study, we introduce and investigate new forms of convergence, namely, P-statistical relative pointwise, uniform, and P-equi-statistical relative convergence, for sequences of functions whose values lie in the space of fuzzy numbers. These notions, motivated by a synthesis of statistical and relative convergence frameworks, are explored both in terms of their structural characteristics and mutual interrelationships. Furthermore, we examine the behavior of their corresponding r-level sets to provide deeper insight into their convergence dynamics. As a principal application, we apply approximation theorems of Korovkin-type for sequences of functions with fuzzy values under the newly proposed modes of convergence, and we compute the rate of convergence.
  • [ X ]
    Öğe
    ℐ-αβ-statistical relative uniform convergence for double sequences and its applications
    (De Gruyter Poland Sp Z O O, 2025) Bayram, Nilay Sahin; Yildiz, Sevda
    This article introduces a novel concept of convergence, referred to as & Iscr; {\mathcal{ {\mathcal I} }} - alpha beta \alpha \beta -statistical relative uniform convergence, for double sequences of functions. This notion, which is proposed for the first time in this article, is explored in depth, leading to the establishment of a Korovkin-type approximation theorem within this framework. The illustrative example demonstrates that the proposed convergence is indeed stronger than previously known forms. Additionally, this article investigates the rate of & Iscr; 2 {{\mathcal{ {\mathcal I} }}}_{2} - alpha beta \alpha \beta -statistical relative uniform convergence, providing explicit computations to support the findings. The results contribute to the understanding of ideal statistical convergence and open up new perspectives for approximation theory.